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Q.

Three identical balls ball-I, ball-II and ball-III are placed on a smooth floor on a straight line at the separation of 10 m between balls as shown in figure. Initially balls are stationary. Ball I is given velocity of 10 m/s towards ball-II. Collision between ball-I and ball-II is inelastic with coefficient of restitution 0.5 but collision between ball-III and II is perfectly elastic. The time interval between two consecutive collisions between ball-I and II is________sec.

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answer is 4.

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Detailed Solution

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mass of each ball be m

$V_{1}, V_{2}$

$\begin{array}{l} e = 0.5 \\ u_{1} = 10 m / s \\ e = \frac{V_{2} - V_{1}}{u_{1} - u_{2}} \\ 0.5 = \frac{V_{2} - V_{1}}{10 - 0} \\ V_{2} - V_{1} = 5 \\ L . C . M \\ m (10) = m (V_{1}) + m (V_{2}) \\ V_{1} + V_{2} = 10 \\ \Rightarrow V_{2} = 7.5 m / s \\ \Rightarrow V_{1} = 2.5 m / s \end{array}$

collision between II & III is elastic, so Ball-II will come to rest and Ball-III will move with a velocity of 7.5m/s.

The time in which the Ball-I reach the Ball-II which is at the point of collision is given by $t = \frac{10}{2.5} = 4 s$

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